Tagged Questions

Questions on more advanced topics of number theory, such as quadratic residues, primitive roots, prime numbers, non-linear Diophantine equations, etc. Consider first if (elementary-number-theory) might be a more appropriate tag before adding this tag.

Can anybody pass me on a good source to see the steps in proving,
\begin{equation}
\zeta(2n) = \frac{(-1)^{k-1}B_2k (2 \pi)^{2k}}{2(2k)!}
\end{equation}
I know how we start by looking at the product ...

I saw this video recently and it suggests that there is some "magical" reason that there are 360 degrees in a circle and that it is also connected with our number system. My question is:
How did we ...

I've looked other questions that might help solve my problem, but haven't found any people who've used my method to solve it. The problem goes like this: Suppose there are 7 men and 5 women, and they ...

Suppose we have a finite amount of numbers $x_1, x_2, ..., x_n$ ($x_i\in\mathbb{N}$) and an object that should be divided into parts in such a way that it can be without further dividing distributed ...

Let $a_1, a_2\dots $ be a sequence of reals such that $a_1 = a_2 = 1$, and
$$a_{n + 2} = \frac{a_{n + 1}^3 + 1}{a_n}$$ for $n \ge 1$. It appears to be the case that all of these values are integers. ...

For completeness I give some definitions. Let $p$ a prime number and consider $V$ a 2-dimensional $\mathbb{F}_p$-vector space.
Consider $k$ a sub-algebra of $\mathrm{End}(V)$ that is a field of $p^2$ ...

Is there a simple analogue of FRACTRAN that maps a natural number to a natural number, instead of mapping a list of fractions to a natural number?
One could use Gödel encoding to translate FRACTRAN ...

Reading through Titchmarh's book on the Riemann Zeta Function, chapter 3 discusses the Prime Number Theorem. One way to prove this result is to check the zeta function has no zeros on the line $z = 1 ...

This is a number theoretical problem that I discovered myself. Let $f(n)$ be the number of factors of $a^n-b^n$ with integer coefficients when its completely factored. For example:
$f(1)=1$, because ...

I was recently cleaning up my laptop when I stumbled upon a spreadsheet that I created a while ago at school when I still had an interest in math. Anyway, I remember reaching the following identity ...

also define $$F^*(n) = \sum_{i=1\,\,(i,n)=1}^n f(\frac in)$$ then prove that $$F^* = \mu * F$$
where $\mu$ is the Möebius function and the $*$ means the Dirichlet convolution.
I tried the Bell series ...